text stringlengths 1 298 |
|---|
6 Conclusion |
Verification of probabilistic forecasts is an essential but complex step of all forecasting procedures. Scoring |
rules may appear as the perfect tool to compare forecast performance since, when proper, they can simulta |
neously assess calibration and sharpness. However, propriety, even if strict, does not ensure that a scoring |
rule is relevant to the problem at hand. With that in mind, we agree with the recommendation of Scheuerer |
and Hamill (2015) that "several different scores be always considered before drawing conclusions". This is |
even more important in a multivariate setting where forecasts are characterized by more complex objects. |
Weproposed a framework to construct proper scoring rules in a multivariate setting using aggregation and |
transformation principles. Aggregation-and-transformation-based scoring rules can improve the conclusions |
27 |
drawn since they enable the verification of specific aspects of the forecast (e.g., anisotropy of the dependence |
structure). This has been illustrated both using examples from the literature and numerical experiments |
showcasing different settings. Moreover, we showed that the aggregation and transformation principles can |
be used to construct scoring rules that are proper, interpretable, and not affected by the double-penalty |
effect. This could be a starting point to help bridging the gap between the proper scoring rule community |
and the spatial verification tools community. |
As the interest for machine learning-based weather forecast is increasing (see, e.g., Ben Bouallègue et al. |
2024a), multiple approaches have performance comparable to ECMWF deterministic high-resolution fore |
casts (Keisler, 2022; Pathak et al., 2022; Bi et al., 2023; Lam et al., 2022; Chen et al., 2023). The natural |
extension to probabilistic forecast is already developing and enabled by publicly available benchmark datasets |
such as WeatherBench 2 (Rasp et al., 2024). Aggregation-and-transformation-based methods can help ensure |
that parameter inference does not hedge certain important aspects of the multivariate probabilistic forecasts. |
There seems to be a trade-off between discrimination ability and strict propriety. Discrimination ability |
comes from the ability of scoring rules to differentiate misspecification of certain characteristics. By defi |
nition, the expectation of strictly proper scoring rules is minimized when the probabilistic forecast is the |
true distribution. Nonetheless, it does not guarantee that this global minimum is steep in any misspecifi |
cation direction. However, interpretable scoring rules can discriminate the misspecification of their target |
characteristic. Should scoring rules discriminating any misspecification be pursued? Or should interpretable |
scoring rules discriminating a specific type of misspecification be used instead? |
Acknowledgments |
The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference |
ANR-20-CE40-0025-01 (T-REX project) and the Energy-oriented Centre of Excellence II (EoCoE-II), Grant |
Agreement 824158, funded within the Horizon2020 framework of the European Union. Part of this work was |
also supported by the ExtremesLearning grant from 80 PRIME CNRS-INSU and this study has received |
funding from Agence Nationale de la Recherche- France 2030 as part of the PEPR TRACCS program under |
grant number ANR-22-EXTR-0005 and the ANR EXSTA. |
Sam Allen is thanked for fruitful discussions during the preparation of this manuscript. |
References |
Paolo Agnolucci, Chrysanthi Rapti, Peter Alexander, Vincenzo De Lipsis, Robert A. Holland, Felix Eigen |
brod, and Paul Ekins. Impacts of rising temperatures and farm management practices on global yields |
of 18 crops. Nature Food, 1(9):562–571, September 2020. ISSN 2662-1355. https://doi.org/10.1038/ |
s43016-020-00148-x. |
Zeina Al Masry, Romain Pic, Clément Dombry, and Chrisine Devalland. A new methodology to predict the |
oncotype scores based on clinico-pathological data with similar tumor profiles. Breast Cancer Research |
and Treatment, 2023. ISSN 1573-7217. https://doi.org/10.1007/s10549-023-07141-5. |
Carol Alexander, Michael Coulon, Y. Han, and Xiaochun Meng. Evaluating the discrimination ability |
of proper multi-variate scoring rules. Annals of Operations Research, March 2022. ISSN 1572-9338. |
ERROR: type should be string, got " https://doi.org/10.1007/s10479-022-04611-9." |
Sam Allen, Jonas Bhend, Olivia Martius, and Johanna Ziegel. Weighted verification tools to evaluate uni |
variate and multivariate probabilistic forecasts for high-impact weather events. Weather and Forecasting, |
38(3):499–516, March 2023a. ISSN 1520-0434. https://doi.org/10.1175/waf-d-22-0161.1. |
Sam Allen, David Ginsbourger, and Johanna Ziegel. Evaluating forecasts for high-impact events using |
transformed kernel scores. SIAM/ASA Journal on Uncertainty Quantification, 11(3):906–940, August |
2023b. ISSN 2166-2525. https://doi.org/10.1137/22m1532184. |
28 |
Sam Allen, Johanna Ziegel, and David Ginsbourger. Assessing the calibration of multivariate probabilistic |
forecasts. Quarterly Journal of the Royal Meteorological Society, 150(760):1315–1335, February 2024. ISSN |
1477-870X. https://doi.org/10.1002/qj.4647. |
Jeffrey L. Anderson. A method for producing and evaluating probabilistic forecasts from ensemble model |
integrations. Journal of Climate, 9(7):1518–1530, July 1996. ISSN 1520-0442. https://doi.org/10. |
1175/1520-0442(1996)009<1518:amfpae>2.0.co;2. |
Andreas Basse-O’Connor, Vytaut˙ e Pilipauskait˙ e, and Mark Podolskij. Power variations for fractional type |
infinitely divisible random fields. Electronic Journal of Probability, 26(none):1– 35, 2021. https://doi. |
org/10.1214/21-EJP617. URL https://doi.org/10.1214/21-EJP617. |
Zied Ben Bouallègue, Mariana C. A. Clare, Linus Magnusson, Estibaliz Gascón, Michael Maier-Gerber, |
Martin Janoušek, Mark Rodwell, Florian Pinault, Jesper S. Dramsch, Simon T. K. Lang, Baudouin |
Raoult, Florence Rabier, Matthieu Chevallier, Irina Sandu, Peter Dueben, Matthew Chantry, and Florian |
Pappenberger. The rise of data-driven weather forecasting: A first statistical assessment of machine |
learning–based weather forecasts in an operational-like context. Bulletin of the American Meteorological |
Society, 105(6):E864–E883, June 2024a. ISSN 1520-0477. https://doi.org/10.1175/bams-d-23-0162. |
1. |
Zied Ben Bouallègue, Jonathan A. Weyn, Mariana C. A. Clare, Jesper Dramsch, Peter Dueben, and Matthew |
Chantry. Improving medium-range ensemble weather forecasts with hierarchical ensemble transformers. |
Artificial Intelligence for the Earth Systems, 3(1), January 2024b. ISSN 2769-7525. https://doi.org/ |
10.1175/aies-d-23-0027.1. |
Albert Benassi, Serge Cohen, and Jacques Istas. On roughness indices for fractional fields. Bernoulli, 10 |
(2):357– 373, 2004. https://doi.org/10.3150/bj/1082380223. URL https://doi.org/10.3150/bj/ |
1082380223. |
Alain Berlinet and Christine Thomas-Agnan. Reproducing kernel Hilbert spaces in probability and statis |
tics. Kluwer Academic Publishers, Boston, MA, 2004. ISBN 1-4020-7679-7. https://doi.org/10.1007/ |
978-1-4419-9096-9. URL https://doi.org/10.1007/978-1-4419-9096-9. With a preface by Persi |
Diaconis. |
Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian. Accurate medium-range |
global weather forecasting with 3d neural networks. Nature, 619(7970):533–538, July 2023. ISSN 1476 |
4687. https://doi.org/10.1038/s41586-023-06185-3. |
Mathias Blicher Bjerregård, Jan Kloppenborg Møller, and Henrik Madsen. An introduction to multivariate |
probabilistic forecast evaluation. Energy and AI, 4:100058, June 2021. ISSN 2666-5468. https://doi. |
org/10.1016/j.egyai.2021.100058. |
David Bolin and Jonas Wallin. Local scale invariance and robustness of proper scoring rules. Statistical |
Science, 38(1), feb 2023. https://doi.org/10.1214/22-sts864. |
Nikos I. Bosse, Sam Abbott, Anne Cori, Edwin van Leeuwen, Johannes Bracher, and Sebastian Funk. Scoring |
epidemiological forecasts on transformed scales. PLOS Computational Biology, 19(8):e1011393, August |
2023. ISSN 1553-7358. https://doi.org/10.1371/journal.pcbi.1011393. |
Jonas Brehmer. Elicitability and its application in risk management. July 2017. https://doi.org/10. |
48550/ARXIV.1707.09604. |
Jonas R. Brehmer and Kirstin Strokorb. Why scoring functions cannot assess tail properties. Electronic |
Journal of Statistics, 13(2), January 2019. ISSN 1935-7524. https://doi.org/10.1214/19-ejs1622. |
John Bjørnar Bremnes. Ensemble postprocessing using quantile function regression based on neural networks |
and bernstein polynomials. Monthly Weather Review, 148(1):403–414, December 2019. ISSN 1520-0493. |
ERROR: type should be string, got " https://doi.org/10.1175/mwr-d-19-0227.1." |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.